A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate s...

and implement high-performance algorithms to compute the discrete Fourier transform (DFT) [17, 24] and matrix multiplication [14, 15] on shared-memory vector multiprocessors. The significance of the tensor product lies in its ability to model both the computational structures occurring in block-recursive algorithms and the underlying hardware structures, such as the interconnection networks [19...

In analogy with the maximal tensor product of C-algebras, we deene the \maximal" tensor product E 1 E 2 of two operator spaces E 1 and E 2 and we show that it can be identiied completely isometrically with the sum of the two Haagerup tensor We also study the extension to more than two factors.

In analogy with the maximal tensor product of C *-algebras, we define the " maximal " tensor product E 1 ⊗ µ E 2 of two operator spaces E 1 and E 2 and we show that it can be identified completely isometrically with the sum of the two Haagerup tensor

This paper gives an overview of notations used in multiway array processing. We redefine the vectorization and matricization operators to comply with some properties of the Kronecker product. The tensor product and Kronecker product are also represented with two different symbols, and it is shown how these notations lead to clearer expressions for multiway array operations. Finally, the paper r...

We propose the tensor Kronecker product singular value decomposition (TKPSVD) that decomposes a real k-way tensor A into a linear combination of tensor Kronecker products with an arbitrary number of d factors A = ∑R j=1 σj A (d) j ⊗ · · · ⊗ A (1) j . We generalize the matrix Kronecker product to tensors such that each factor A j in the TKPSVD is a k-way tensor. The algorithm relies on reshaping...

Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.

Information on su(N) tensor product multiplicities is neatly encoded in Berenstein-Zelevinsky triangles. Here we study a generalisation of these triangles by allowing negative as well as positive integer entries. For a fixed triple product of weights, these generalised Berenstein-Zelevinsky triangles span a lattice in which one may move by adding integer linear combinations of so-called virtual...

Information on su(N) tensor product multiplicities is neatly encoded in Berenstein-Zelevinsky triangles. Here we study a generalisation of these triangles by allowing negative as well as non-negative integer entries. For a fixed triple product of weights, these generalised Berenstein-Zelevinsky triangles span a lattice in which one may move by adding integer linear combinations of so-called vir...

Information on su(N) tensor product multiplicities is neatly encoded in Berenstein-Zelevinsky triangles. Here we study a generalisation of these triangles by allowing negative as well as positive integer entries. For a fixed triple product of weights, these generalised Berenstein-Zelevinsky triangles span a lattice in which one may move by adding integer linear combinations of so-called virtual...